### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Centre for Telematics and Information Technology (CTIT) |

Number of pages | 39 |

Publication status | Published - Mar 2013 |

### Publication series

Name | CTIT Technical Report Series |
---|---|

Publisher | University of Twente, Centre for Telematica and Information Technology (CTIT) |

No. | TR-CTIT-13-08 |

ISSN (Print) | 1381-3625 |

### Keywords

- IR-85339
- METIS-296384
- EWI-23233
- EC Grant Agreement nr.: FP7/2007-2013
- EC Grant Agreement nr.: FP7/318490

### Cite this

*Divergent Quiescent Transition Systems (extended version)*. (CTIT Technical Report Series; No. TR-CTIT-13-08). Enschede: Centre for Telematics and Information Technology (CTIT).

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*Divergent Quiescent Transition Systems (extended version)*. CTIT Technical Report Series, no. TR-CTIT-13-08, Centre for Telematics and Information Technology (CTIT), Enschede.

**Divergent Quiescent Transition Systems (extended version).** / Stokkink, W.G.J.; Timmer, Mark; Stoelinga, Mariëlle Ida Antoinette.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Divergent Quiescent Transition Systems (extended version)

AU - Stokkink, W.G.J.

AU - Timmer, Mark

AU - Stoelinga, Mariëlle Ida Antoinette

N1 - eemcs-eprint-23233

PY - 2013/3

Y1 - 2013/3

N2 - Quiescence is a fundamental concept in modelling system behaviour, as it explicitly represents the fact that no output is produced in certain states. The notion of quiescence is also essential to model-based testing: if a particular implementation under test does not provide any output, then the test evaluation algorithm must decide whether or not to allow this behaviour. To explicitly model quiescence in all its glory, we introduce Divergent Quiescent Transition Systems (DQTSs). DQTSs model quiescence using explicit delta-labelled transitions, analogous to Suspension Automata (SAs) in the well-known ioco framework. Whereas SAs have only been defined implicitly, DQTSs for the first time provide a fully-formalised framework for quiescence. Also, while SAs are restricted to convergent systems (i.e., without tau-cycles), we show how quiescence can be treated naturally using a notion of fairness, allowing systems exhibiting divergence to be modelled as well. We study compositionality under the familiar automata-theoretical operations of determinisation, parallel composition and action hiding. We provide a non-trivial algorithm for detecting divergent states, and discuss its complexity. Finally, we show how to use DQTSs in the context of model-based testing, for the first time presenting a full-fledged theory that allows ioco to be applied to divergent systems.

AB - Quiescence is a fundamental concept in modelling system behaviour, as it explicitly represents the fact that no output is produced in certain states. The notion of quiescence is also essential to model-based testing: if a particular implementation under test does not provide any output, then the test evaluation algorithm must decide whether or not to allow this behaviour. To explicitly model quiescence in all its glory, we introduce Divergent Quiescent Transition Systems (DQTSs). DQTSs model quiescence using explicit delta-labelled transitions, analogous to Suspension Automata (SAs) in the well-known ioco framework. Whereas SAs have only been defined implicitly, DQTSs for the first time provide a fully-formalised framework for quiescence. Also, while SAs are restricted to convergent systems (i.e., without tau-cycles), we show how quiescence can be treated naturally using a notion of fairness, allowing systems exhibiting divergence to be modelled as well. We study compositionality under the familiar automata-theoretical operations of determinisation, parallel composition and action hiding. We provide a non-trivial algorithm for detecting divergent states, and discuss its complexity. Finally, we show how to use DQTSs in the context of model-based testing, for the first time presenting a full-fledged theory that allows ioco to be applied to divergent systems.

KW - IR-85339

KW - METIS-296384

KW - EWI-23233

KW - EC Grant Agreement nr.: FP7/2007-2013

KW - EC Grant Agreement nr.: FP7/318490

M3 - Report

T3 - CTIT Technical Report Series

BT - Divergent Quiescent Transition Systems (extended version)

PB - Centre for Telematics and Information Technology (CTIT)

CY - Enschede

ER -